"Frequency distribution of the variances"

I am working on a homework assignment from a very vague, unhelpful professor.

I flipped 20 coins, measured the amount of heads and so forth, and repeated this 100 times.

One of the questions involves breaking the 100 measurements of "heads" into 25 groups, where group one is the first 4 measurements, group two is the next 4, and so on. The mean and standard deviation of each group was then found.

I am now asked to "calculate the frequency distribution of the variances of the groups", which I do not understand how to do. I believe they follow a chi-squared distribution, and upon asking the professor I received an unhelpful reply.

I already made a histogram of the experimental frequency distribution of the variances. I now need to find a calculated, theoretical frequency distribution of these variances.

How would I go about analyzing this? I am thoroughly lost on this question.

Your 4 coinflips (denoted here by X) will yield an expected value of 2 times head with a very, very approximated normal distribution of the values 0-4 for this event X. However, the sample sice is very small so that I would not use this approximation. However, if you take the variance of this random variable you get the sum of (X -2)^2 which is indeed chi-squared distributed if you claim your approximation to be valid. Considering your degrees of freedom you should be able to compute your theoretical distribution by chi-squared.

The Chi-squared distribution is defined as the sum of squared standard normal distributions. To standardize a random variable, you substract the expected value of it and then divide by the s.d. Thus: ((X -2)/s.d.)^2 (forgot the s.d. before, sorry) These standardized normal distributions describe each group of coinflips. However, after computing the standard normal deviation, the squared sums of these standard normal deviations should reflect the distribution of all your coinflips (a distribution of the particular groups that you looked at. However, it is only a very rough approximation.